Sometimes, the game will auto-identify an object after you or a monster does something with it. This is a contraction for automatically identify, and means that you identified a type of object without explicitly using the scroll of identify or spellbook of identify. Common ways to auto-identify an object include the engrave-testing of wands, letting monsters use certain objects, and (to possibly dangerous effect) yourself using an unidentified object.
Your character now recognizes that type of object; it adds the object to the list of discoveries that appears when you press [\].
For example, when you hear a monster read an unfamiliar spell scroll, then see the monster teleport away, we say that the game has auto-identified the scroll of teleportation. Now, you know which other scrolls (in your inventory or elsewhere) are scrolls of teleportation, and you saved a scroll of identify in learning this.
You might still think that you know the identity of an object, even if NetHack did not auto-identify it. Suppose that you wore an unidentified ring and quaffed a potion of enlightenment to discover that it gave you cold resistance, or you dropped the ring in a sink and compared the message with a spoiler. You might know what kind of ring it is, even when the game does not tell you. In these cases, the game will still label the item with its randomized appearance, but you can use the (N)ame command to name it yourself. (e.g. the game might still describe that ring of cold resistance as "an engagement ring" but you can (N)ame it "cold resistance" and from then on all engagement rings would be labeled "cold resistance")